${30}^o$

$\frac{30}{360}\cdot \pi {\text{r}}^2=\frac{1}{12}\cdot \pi {12}^2{\text{cm}}^2=\frac{1}{12}\cdot 144\pi {\text{cm}}^2=12\pi {\text{cm}}^2$

 

${45}^o$

$\frac{45}{360}\cdot {12}^2{\text{cm}}^2\pi =\frac{1}{8}\cdot 144\pi {\text{cm}}^2=18\pi {\text{cm}}^2$

 

${90}^o$

$\frac{90}{360}\cdot \pi {\text{r}}^2=\frac{1}{4}\cdot \pi \cdot {12}^2=\frac{1}{4}\cdot 144\pi {\text{cm}}^2=36\pi {\text{cm}}^2$

 

${135}^o$

$\frac{135}{360}\cdot {12}^2{\text{cm}}^2\pi =\frac{3}{8}\cdot 144\pi {\text{cm}}^2=54\pi {\text{cm}}^2$

 

${240}^o$

$\frac{240}{360}\cdot {12}^2\pi {\text{cm}}^2=\frac{2}{3}\cdot 144\pi {\text{cm}}^2=96\pi {\text{cm}}^2$

 

${270}^o$

$\frac{270}{360}\cdot {12}^2\pi {\text{cm}}^2=\frac{3}{4}\cdot 144\pi {\text{cm}}^2=108\pi {\text{cm}}^2$